Can someone help me, my homework is due Monday. If nobody answers correctly before Monday, my teacher will go over the problem in class and I will write the correct answer in the comments. Thank you to anyone who actually helps. There are 2 Senators from each of 50 states. We wish to make a 3-Senator committee in which no two members are from the same state. How many ways can we choose a Senator from a chosen state?

Step-by-step explanation:

We can use probability functions here to try and solve this problem.

We want to find how many ways to choose a senator from a chosen state. Note the "from a chosen state," meaning that it is not asking for how many ways to choose two senators from all 50 states but how to choose 1 from a chosen state (1 chosen state).

Let's calculate all possible values for each scenario.

We can either chose Senator A or Senator B for one state, since there are only two options available

This gives us a total of two possibilities to choose a senator from one state.

The number of ways to choose 3 states being represented, we can use the combinations formula. We can write it as ₅₀C₃, which can be solved using the formula:

Where n is the total number of objects to choose from, and r is how many we want to choose.

Substituting in:

Hence, there are 19,600 ways to choose 3 states from 50 total.

The total number of possible combinations to choose three senators from 50 states, none of the states being equal, we can multiply the number of ways to pick 3 states from 50 (19600) and multiply it by since there are 3 members in the Senate and two Senators in each state.

Hence, there are 156,800 ways to make a 3-senator committee with no member from the same state (2 senators per state).

However, let's look back at what the problem is asking.

"How many ways can we choose a Senator from a chosen state?"

Put simply - assuming we chose a state, how many ways can we select a senator from that state?

We answered that in Part 1! We ended up getting two ways, as there are two senators.

Therefore, the answer to your problem is 2 ways.

Hope this helped!